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What is my age (expressed as a positive integer)? Although [#permalink]

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10 Oct 2012, 12:25

1

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00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

34% (02:47) correct
66% (01:44) wrong based on 35 sessions

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I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes... Contemplating my age, I just realized that the integer number that represents my age has some very nice properties )

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares. (2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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10 Oct 2012, 14:11

Evajager,

I got the right answer but I am abit unsure on statement 2. Could you solve the question. I understand if you waiting for others to post first.

I am abit unclear on this part of the statement (2) My age can be written as the product of a two digit integer and the sum of its digits. _________________

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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10 Oct 2012, 14:53

I am posting here for the first time as I joined GMAT club recently.

If we take statement (2) then according to that i took two digit integer as 13 and the sum of it's digits is 4( which is a perfect square) so the product of 13 and 4 = 52.

now according to statement first 16( which is a perfect square)+ 36( which is also a perfect square) = 52 which is the age in two digits.

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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10 Oct 2012, 14:59

geno5 wrote:

Evajager,

I got the right answer but I am abit unsure on statement 2. Could you solve the question. I understand if you waiting for others to post first.

I am abit unclear on this part of the statement (2) My age can be written as the product of a two digit integer and the sum of its digits.

You guys, just being too polite, don't want to reveal my age. Well, it seems that I have no choice, I have to do it...

(1) Obviously not sufficient. Too many options: 4 + 25 = 29, 9 + 25 = 34, 4 + 36 = 40... (wishful thinking)

(2) My age is (A + B)AB, where AB is a two digit number, A and B are distinct, and A + B is a perfect square. Possible solutions: AB = 10, (1 + 0)*10 = 10. 4*13 =52 (4*31 = 124 > 100) Next perfect square is 9. But any two digits with sum 9, when multiplied by 9, will give a number greater than 100. 9*18 is the smallest and already greater than 100.

So, we are left with two possibilities: 10 and 52.

(1) and (2) together: 10 = 1 + 9 and 52 = 16 + 36, both are sums of two perfect squares. So, the answer should be E. If we take into account that I am an adult, then B should be the answer.

I cannot full you anymore...I am 52 years old.

Just a short summary of the properties of the number 52: \(52 = 4*13\) \(,\,\,\,4=2^2\) and \(4 = 1 + 3.\) \(52 = 16 + 36 = 4^2+6^2\), sum of two consecutive even squares. \(13 = 4 + 9 = 2^2+3^2\), sum of two consecutive squares.

Can you find some more?

Next year is going to be 53. Prime number. Until now, I just found that \(53=6\cdot{9}-1=(2\cdot{3})\cdot{3^2}-1.\)
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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10 Oct 2012, 15:42

aah123 wrote:

I am posting here for the first time as I joined GMAT club recently.

If we take statement (2) then according to that i took two digit integer as 13 and the sum of it's digits is 4( which is a perfect square) so the product of 13 and 4 = 52.

now according to statement first 16( which is a perfect square)+ 36( which is also a perfect square) = 52 which is the age in two digits.

so the answer is C

Welcome to the Club! This is not a real GMAT test question, I was just trying to fool the club members...

I guess you didn't consider 10 as a possible solution for (2). But you are right, I am 52. And as formulated, the answer to the question is either B or E, depending on whether we regard 10 as a possible solution or not.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 11:36

EvaJager wrote:

I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes... Contemplating my age, I just realized that the integer number that represents my age has some very nice properties )

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares. (2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.

EvaJager is 52.

Answer would be E.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18. so, we need to consider squares < 18 ie 1,4,9 and 16. let the age be ab => (10a+b)(a+b) = age. where a+b = perfect square.

for a+b=1 ; ab=10 for a+b=4 ; ab = 13 and 31 (since digits are distinct) for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with: 10*1 = 10 13*4 = 52 31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52. 10 = 1^2 + 3^2 52 = 6^2+4^2

hence, the age can be 52 or 10. So E.
_________________

Illegitimi non carborundum.

Last edited by thefibonacci on 26 Feb 2014, 14:16, edited 1 time in total.

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 12:20

1

This post received KUDOS

thefibonacci wrote:

EvaJager wrote:

I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes... Contemplating my age, I just realized that the integer number that represents my age has some very nice properties )

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares. (2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.

EvaJager is 52.

Answer would be C.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18. so, we need to consider squares < 18 ie 1,4,9 and 16. let the age be ab => (10a+b)(a+b) = age. where a+b = perfect square.

for a+b=1 ; ab=10 for a+b=4 ; ab = 13 and 31 (since digits are distinct) for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with: 10*1 = 10 13*4 = 52 31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52. 10 cannot be expressed in the form of x^2+y^2 52 = 6^2+4^2

hence, the age is 52....which can be found by combining both the fact statements.

\(10=1^2+3^2\)
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: What is my age (expressed as a positive integer)? Although [#permalink]

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26 Feb 2014, 14:15

EvaJager wrote:

thefibonacci wrote:

EvaJager wrote:

I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes... Contemplating my age, I just realized that the integer number that represents my age has some very nice properties )

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares. (2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.

EvaJager is 52.

Answer would be C.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18. so, we need to consider squares < 18 ie 1,4,9 and 16. let the age be ab => (10a+b)(a+b) = age. where a+b = perfect square.

for a+b=1 ; ab=10 for a+b=4 ; ab = 13 and 31 (since digits are distinct) for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with: 10*1 = 10 13*4 = 52 31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52. 10 cannot be expressed in the form of x^2+y^2 52 = 6^2+4^2

hence, the age is 52....which can be found by combining both the fact statements.

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